A modularity test for elliptic mirror symmetry

Abstract

In this note a prediction of an algebraic mirror construction is checked for elliptic curves of Brieskorn-Pham type via number theoretic methods. It is shown that the modular forms associated to the Hasse-Weil L-series of mirror pairs of such curves are identical.

11 pages

References in corpus (10)

• Landau-Ginzburg String Vacua
• No Mirror Symmetry in Landau-Ginzburg Spectra!
• Duality in String Theory
• Conifold Transitions and Mirror Symmetries
• The Arithmetic of Calabi--Yau Manifolds and Mirror Symmetry
• The Langlands Program and String Modular K3 Surfaces
• The Shimura-Taniyama Conjecture and Conformal Field Theory
• Arithmetic Spacetime Geometry from String Theory
• Geometric Kac-Moody Modularity
• Motives and mirror symmetry for Calabi-Yau orbifolds

Cited by in corpus (4)

• Emergent spacetime from modular motives
• String-theory Realization of Modular Forms for Elliptic Curves with Complex Multiplication
• Motivic L-Function Identities from CFT and Arithmetic Mirror Symmetry
• Emergent spacetime and black hole probes from automorphic forms